Algebraic Bethe Ansatz for Integrable Extended Hubbard Models Arising from Supersymmetric Group Solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.Comment: 15 pages, RevTex, No figures, to be published in J. Phys.

Open t-J chain with boundary impurities

We study integrable boundary conditions for the supersymmetric t-J model of correlated electrons which arise when combining static scattering potentials with dynamical impurities carrying an internal degree of freedom. The latter differ from the bulk sites by allowing for double occupation of the local orbitals. The spectrum of the resulting Hamiltonians is obtained by means of the algebraic Bethe Ansatz.Comment: LaTeX2e, 9p

Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.Comment: 24 pages and 3 eps figures, Revtex, accepted for publication in J. Phys.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe

Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.Comment: Latex file, 27 pages, 5 figures (.eps) A more detailed study of the representations allowing string hypothesis has added. A simpler formula for the densities is given. References added and misprint correcte

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone

Neutrino oscillation experiments and limits on lepton-number and lepton-flavor violating processes

Using a three neutrino framework we investigate bounds for the effective Majorana neutrino mass matrix. The mass measured in neutrinoless double beta decay is its (11) element. Lepton-number and -flavor violating processes sensitive to each element are considered and limits on branching ratios or cross sections are given. Those processes include $\mu^- e^+$ conversion, $K^+ \to \pi^- \mu^+ \mu^+$ or recently proposed high-energy scattering processes at HERA. Including all possible mass schemes, the three solar solutions and other allowed possibilities, there is a total of 80 mass matrices. The obtained indirect limits are up to 14 orders of magnitude more stringent than direct ones. It is investigated how neutrinoless double beta decay may judge between different mass and mixing schemes as well as solar solutions. Prospects for detecting processes depending on elements of the mass matrix are also discussed.Comment: 16 pages, 2 figure

A comparison of genomic profiles of complex diseases under different models

Background: Various approaches are being used to predict individual risk to polygenic diseases from data provided by genome-wide association studies. As there are substantial differences between the diseases investigated, the data sets used and the way they are tested, it is difficult to assess which models are more suitable for this task. Results: We compared different approaches for seven complex diseases provided by the Wellcome Trust Case Control Consortium (WTCCC) under a within-study validation approach. Risk models were inferred using a variety of learning machines and assumptions about the underlying genetic model, including a haplotype-based approach with different haplotype lengths and different thresholds in association levels to choose loci as part of the predictive model. In accordance with previous work, our results generally showed low accuracy considering disease heritability and population prevalence. However, the boosting algorithm returned a predictive area under the ROC curve (AUC) of 0.8805 for Type 1 diabetes (T1D) and 0.8087 for rheumatoid arthritis, both clearly over the AUC obtained by other approaches and over 0.75, which is the minimum required for a disease to be successfully tested on a sample at risk, which means that boosting is a promising approach. Its good performance seems to be related to its robustness to redundant data, as in the case of genome-wide data sets due to linkage disequilibrium. Conclusions: In view of our results, the boosting approach may be suitable for modeling individual predisposition to Type 1 diabetes and rheumatoid arthritis based on genome-wide data and should be considered for more in-depth research.This work was supported by the Spanish Secretary of Research, Development and Innovation [TIN2010-20900-C04-1]; the Spanish Health Institute Carlos III [PI13/02714]and [PI13/01527] and the Andalusian Research Program under project P08-TIC-03717 with the help of the European Regional Development Fund (ERDF). The authors are very grateful to the reviewers, as they believe that their comments have helped to substantially improve the quality of the paper

Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets

It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of {\fR}^2. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted proof of existence of a "universal" area-preserving map $F_*$ -- a map with orbits of all binary periods 2^k, k \in \fN. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics. We first demonstrate that the map $F_*$ admits a "bi-infinite heteroclinic tangle": a sequence of periodic points $\{z_k\}$, k \in \fZ, |z_k| \converge{{k \to \infty}} 0, \quad |z_k| \converge{{k \to -\infty}} \infty, whose stable and unstable manifolds intersect transversally; and, for any N \in \fN, a compact invariant set on which $F_*$ is homeomorphic to a topological Markov chain on the space of all two-sided sequences composed of $N$ symbols. A corollary of these results is the existence of {\it unbounded} and {\it oscillating} orbits. We also show that the third iterate for all maps close to $F_*$ admits a horseshoe. We use distortion tools to provide rigorous bounds on the Hausdorff dimension of the associated locally maximal invariant hyperbolic set: $$ 0.7673 \ge {\rm dim}_H(\cC_F) \ge \varepsilon \approx 0.00044 e^{-1797}.$